Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+5y &= 1 \\ 3x+5y &= -5\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $5y = -3x-5$ Divide both sides by $5$ to isolate $y$ $y = {-\dfrac{3}{5}x - 1}$ Substitute this expression for $y$ in the first equation. $6x+5({-\dfrac{3}{5}x - 1}) = 1$ $6x - 3x - 5 = 1$ Simplify by combining terms, then solve for $x$ $3x - 5 = 1$ $3x = 6$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $6( 2)+5y = 1$ $12+5y = 1$ $5y = -11$ $y = -\dfrac{11}{5}$ The solution is $\enspace x = 2, \enspace y = -\dfrac{11}{5}$.